Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(301,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.301");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.n (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.13140625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 751.2 | ||
Root | \(-0.227943 + 0.701538i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.751 |
Dual form | 825.2.n.g.301.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.212253 | + | 0.154211i | −0.150086 | + | 0.109044i | −0.660294 | − | 0.751007i | \(-0.729568\pi\) |
0.510208 | + | 0.860051i | \(0.329568\pi\) | |||||||
\(3\) | −0.309017 | − | 0.951057i | −0.178411 | − | 0.549093i | ||||
\(4\) | −0.596764 | + | 1.83665i | −0.298382 | + | 0.918325i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.212253 | + | 0.154211i | 0.0866521 | + | 0.0629564i | ||||
\(7\) | 0.986854 | − | 3.03722i | 0.372996 | − | 1.14796i | −0.571825 | − | 0.820376i | \(-0.693764\pi\) |
0.944821 | − | 0.327587i | \(-0.106236\pi\) | |||||||
\(8\) | −0.318714 | − | 0.980901i | −0.112682 | − | 0.346801i | ||||
\(9\) | −0.809017 | + | 0.587785i | −0.269672 | + | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.27115 | − | 0.547326i | 0.986289 | − | 0.165025i | ||||
\(12\) | 1.93117 | 0.557480 | ||||||||
\(13\) | −0.905781 | + | 0.658088i | −0.251218 | + | 0.182521i | −0.706267 | − | 0.707946i | \(-0.749622\pi\) |
0.455048 | + | 0.890467i | \(0.349622\pi\) | |||||||
\(14\) | 0.258911 | + | 0.796845i | 0.0691968 | + | 0.212966i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.90578 | − | 2.11117i | −0.726445 | − | 0.527793i | ||||
\(17\) | −0.0713767 | − | 0.0518582i | −0.0173114 | − | 0.0125775i | 0.579096 | − | 0.815259i | \(-0.303406\pi\) |
−0.596407 | + | 0.802682i | \(0.703406\pi\) | |||||||
\(18\) | 0.0810736 | − | 0.249519i | 0.0191092 | − | 0.0588122i | ||||
\(19\) | −0.0212704 | − | 0.0654637i | −0.00487977 | − | 0.0150184i | 0.948587 | − | 0.316517i | \(-0.102513\pi\) |
−0.953467 | + | 0.301498i | \(0.902513\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.19353 | −0.696885 | ||||||||
\(22\) | −0.609909 | + | 0.620620i | −0.130033 | + | 0.132317i | ||||
\(23\) | −6.65450 | −1.38756 | −0.693780 | − | 0.720187i | \(-0.744056\pi\) | ||||
−0.693780 | + | 0.720187i | \(0.744056\pi\) | |||||||
\(24\) | −0.834404 | + | 0.606230i | −0.170322 | + | 0.123746i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.0907705 | − | 0.279363i | 0.0178016 | − | 0.0547876i | ||||
\(27\) | 0.809017 | + | 0.587785i | 0.155695 | + | 0.113119i | ||||
\(28\) | 4.98940 | + | 3.62501i | 0.942908 | + | 0.685062i | ||||
\(29\) | 1.15444 | − | 3.55299i | 0.214373 | − | 0.659773i | −0.784824 | − | 0.619718i | \(-0.787247\pi\) |
0.999197 | − | 0.0400546i | \(-0.0127532\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.75430 | − | 5.63383i | 1.39271 | − | 1.01187i | 0.397152 | − | 0.917753i | \(-0.369998\pi\) |
0.995562 | − | 0.0941130i | \(-0.0300015\pi\) | |||||||
\(32\) | 3.00509 | 0.531230 | ||||||||
\(33\) | −1.53138 | − | 2.94192i | −0.266579 | − | 0.512122i | ||||
\(34\) | 0.0231471 | 0.00396969 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.596764 | − | 1.83665i | −0.0994606 | − | 0.306108i | ||||
\(37\) | 2.57418 | − | 7.92250i | 0.423192 | − | 1.30245i | −0.481523 | − | 0.876433i | \(-0.659916\pi\) |
0.904715 | − | 0.426017i | \(-0.140084\pi\) | |||||||
\(38\) | 0.0146100 | + | 0.0106148i | 0.00237005 | + | 0.00172194i | ||||
\(39\) | 0.905781 | + | 0.658088i | 0.145041 | + | 0.105378i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.60489 | − | 11.0947i | −0.562989 | − | 1.73270i | −0.673852 | − | 0.738866i | \(-0.735362\pi\) |
0.110863 | − | 0.993836i | \(-0.464638\pi\) | |||||||
\(42\) | 0.677837 | − | 0.492478i | 0.104593 | − | 0.0759909i | ||||
\(43\) | 11.8217 | 1.80280 | 0.901399 | − | 0.432989i | \(-0.142541\pi\) | ||||
0.901399 | + | 0.432989i | \(0.142541\pi\) | |||||||
\(44\) | −0.946857 | + | 6.33458i | −0.142744 | + | 0.954974i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.41244 | − | 1.02620i | 0.208253 | − | 0.151305i | ||||
\(47\) | −0.280594 | − | 0.863579i | −0.0409288 | − | 0.125966i | 0.928504 | − | 0.371322i | \(-0.121095\pi\) |
−0.969433 | + | 0.245356i | \(0.921095\pi\) | |||||||
\(48\) | −1.10991 | + | 3.41595i | −0.160202 | + | 0.493050i | ||||
\(49\) | −2.58773 | − | 1.88010i | −0.369676 | − | 0.268586i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.0272635 | + | 0.0839083i | −0.00381765 | + | 0.0117495i | ||||
\(52\) | −0.668140 | − | 2.05632i | −0.0926544 | − | 0.285161i | ||||
\(53\) | 0.705768 | − | 0.512771i | 0.0969447 | − | 0.0704344i | −0.538257 | − | 0.842781i | \(-0.680917\pi\) |
0.635202 | + | 0.772346i | \(0.280917\pi\) | |||||||
\(54\) | −0.262360 | −0.0357026 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.29374 | −0.440144 | ||||||||
\(57\) | −0.0556868 | + | 0.0404588i | −0.00737589 | + | 0.00535890i | ||||
\(58\) | 0.302877 | + | 0.932160i | 0.0397697 | + | 0.122399i | ||||
\(59\) | 0.567369 | − | 1.74618i | 0.0738651 | − | 0.227333i | −0.907307 | − | 0.420469i | \(-0.861866\pi\) |
0.981172 | + | 0.193135i | \(0.0618656\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.13881 | + | 5.91319i | 1.04207 | + | 0.757107i | 0.970688 | − | 0.240342i | \(-0.0772597\pi\) |
0.0713799 | + | 0.997449i | \(0.477260\pi\) | |||||||
\(62\) | −0.777078 | + | 2.39160i | −0.0986890 | + | 0.303733i | ||||
\(63\) | 0.986854 | + | 3.03722i | 0.124332 | + | 0.382654i | ||||
\(64\) | 5.17372 | − | 3.75893i | 0.646715 | − | 0.469866i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.778717 | + | 0.388276i | 0.0958534 | + | 0.0477935i | ||||
\(67\) | −9.53916 | −1.16539 | −0.582697 | − | 0.812690i | \(-0.698003\pi\) | ||||
−0.582697 | + | 0.812690i | \(0.698003\pi\) | |||||||
\(68\) | 0.137840 | − | 0.100147i | 0.0167156 | − | 0.0121446i | ||||
\(69\) | 2.05635 | + | 6.32881i | 0.247556 | + | 0.761899i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.77370 | + | 2.74175i | 0.447855 | + | 0.325386i | 0.788748 | − | 0.614716i | \(-0.210729\pi\) |
−0.340893 | + | 0.940102i | \(0.610729\pi\) | |||||||
\(72\) | 0.834404 | + | 0.606230i | 0.0983354 | + | 0.0714449i | ||||
\(73\) | 2.21267 | − | 6.80989i | 0.258973 | − | 0.797037i | −0.734048 | − | 0.679098i | \(-0.762371\pi\) |
0.993021 | − | 0.117939i | \(-0.0376288\pi\) | |||||||
\(74\) | 0.675360 | + | 2.07854i | 0.0785090 | + | 0.241626i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.132927 | 0.0152478 | ||||||||
\(77\) | 1.56580 | − | 10.4754i | 0.178439 | − | 1.19378i | ||||
\(78\) | −0.293740 | −0.0332595 | ||||||||
\(79\) | −0.640209 | + | 0.465139i | −0.0720292 | + | 0.0523323i | −0.623217 | − | 0.782049i | \(-0.714175\pi\) |
0.551188 | + | 0.834381i | \(0.314175\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | 2.47608 | + | 1.79898i | 0.273437 | + | 0.198664i | ||||
\(83\) | 0.200012 | + | 0.145318i | 0.0219542 | + | 0.0159507i | 0.598708 | − | 0.800967i | \(-0.295681\pi\) |
−0.576754 | + | 0.816918i | \(0.695681\pi\) | |||||||
\(84\) | 1.90578 | − | 5.86539i | 0.207938 | − | 0.639966i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.50920 | + | 1.82304i | −0.270574 | + | 0.196584i | ||||
\(87\) | −3.73583 | −0.400523 | ||||||||
\(88\) | −1.57943 | − | 3.03423i | −0.168368 | − | 0.323450i | ||||
\(89\) | −14.5788 | −1.54535 | −0.772673 | − | 0.634804i | \(-0.781081\pi\) | ||||
−0.772673 | + | 0.634804i | \(0.781081\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.10489 | + | 3.40050i | 0.115824 | + | 0.356469i | ||||
\(92\) | 3.97116 | − | 12.2220i | 0.414022 | − | 1.27423i | ||||
\(93\) | −7.75430 | − | 5.63383i | −0.804084 | − | 0.584201i | ||||
\(94\) | 0.192730 | + | 0.140027i | 0.0198786 | + | 0.0144427i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.928623 | − | 2.85801i | −0.0947772 | − | 0.291694i | ||||
\(97\) | −3.31048 | + | 2.40521i | −0.336128 | + | 0.244212i | −0.743027 | − | 0.669262i | \(-0.766610\pi\) |
0.406898 | + | 0.913474i | \(0.366610\pi\) | |||||||
\(98\) | 0.839188 | 0.0847708 | ||||||||
\(99\) | −2.32471 | + | 2.36553i | −0.233642 | + | 0.237745i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.47207 | + | 2.52261i | −0.345484 | + | 0.251009i | −0.746972 | − | 0.664856i | \(-0.768493\pi\) |
0.401488 | + | 0.915864i | \(0.368493\pi\) | |||||||
\(102\) | −0.00715284 | − | 0.0220142i | −0.000708236 | − | 0.00217973i | ||||
\(103\) | −0.646712 | + | 1.99038i | −0.0637224 | + | 0.196118i | −0.977849 | − | 0.209311i | \(-0.932878\pi\) |
0.914127 | + | 0.405429i | \(0.132878\pi\) | |||||||
\(104\) | 0.934204 | + | 0.678739i | 0.0916062 | + | 0.0665558i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.0707268 | + | 0.217675i | −0.00686959 | + | 0.0211424i | ||||
\(107\) | 4.86421 | + | 14.9705i | 0.470241 | + | 1.44725i | 0.852270 | + | 0.523103i | \(0.175226\pi\) |
−0.382029 | + | 0.924151i | \(0.624774\pi\) | |||||||
\(108\) | −1.56235 | + | 1.13511i | −0.150337 | + | 0.109226i | ||||
\(109\) | −4.13271 | −0.395842 | −0.197921 | − | 0.980218i | \(-0.563419\pi\) | ||||
−0.197921 | + | 0.980218i | \(0.563419\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.33021 | −0.790668 | ||||||||
\(112\) | −9.27969 | + | 6.74209i | −0.876848 | + | 0.637067i | ||||
\(113\) | −4.25053 | − | 13.0818i | −0.399856 | − | 1.23063i | −0.925114 | − | 0.379688i | \(-0.876031\pi\) |
0.525258 | − | 0.850943i | \(-0.323969\pi\) | |||||||
\(114\) | 0.00558051 | − | 0.0171750i | 0.000522662 | − | 0.00160859i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.83666 | + | 4.24059i | 0.541921 | + | 0.393728i | ||||
\(117\) | 0.345977 | − | 1.06481i | 0.0319856 | − | 0.0984416i | ||||
\(118\) | 0.148855 | + | 0.458127i | 0.0137032 | + | 0.0421740i | ||||
\(119\) | −0.227943 | + | 0.165611i | −0.0208955 | + | 0.0151815i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.4009 | − | 3.58078i | 0.945533 | − | 0.325525i | ||||
\(122\) | −2.63937 | −0.238957 | ||||||||
\(123\) | −9.43772 | + | 6.85690i | −0.850971 | + | 0.618266i | ||||
\(124\) | 5.71989 | + | 17.6040i | 0.513661 | + | 1.58089i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.677837 | − | 0.492478i | −0.0603865 | − | 0.0438734i | ||||
\(127\) | 6.39106 | + | 4.64338i | 0.567115 | + | 0.412033i | 0.834056 | − | 0.551680i | \(-0.186013\pi\) |
−0.266941 | + | 0.963713i | \(0.586013\pi\) | |||||||
\(128\) | −2.37572 | + | 7.31171i | −0.209986 | + | 0.646270i | ||||
\(129\) | −3.65312 | − | 11.2431i | −0.321639 | − | 0.989903i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.3539 | −1.42884 | −0.714422 | − | 0.699715i | \(-0.753310\pi\) | ||||
−0.714422 | + | 0.699715i | \(0.753310\pi\) | |||||||
\(132\) | 6.31714 | − | 1.05698i | 0.549837 | − | 0.0919982i | ||||
\(133\) | −0.219819 | −0.0190607 | ||||||||
\(134\) | 2.02472 | − | 1.47104i | 0.174909 | − | 0.127079i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.0281190 | + | 0.0865414i | −0.00241118 | + | 0.00742086i | ||||
\(137\) | 6.25538 | + | 4.54480i | 0.534433 | + | 0.388289i | 0.822013 | − | 0.569468i | \(-0.192851\pi\) |
−0.287580 | + | 0.957757i | \(0.592851\pi\) | |||||||
\(138\) | −1.41244 | − | 1.02620i | −0.120235 | − | 0.0873558i | ||||
\(139\) | 6.23796 | − | 19.1985i | 0.529097 | − | 1.62839i | −0.226972 | − | 0.973901i | \(-0.572883\pi\) |
0.756069 | − | 0.654492i | \(-0.227117\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.734604 | + | 0.533721i | −0.0618648 | + | 0.0449474i | ||||
\(142\) | −1.22379 | −0.102698 | ||||||||
\(143\) | −2.60276 | + | 2.64846i | −0.217653 | + | 0.221476i | ||||
\(144\) | 3.59174 | 0.299312 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.580514 | + | 1.78664i | 0.0480437 | + | 0.147863i | ||||
\(147\) | −0.988426 | + | 3.04206i | −0.0815240 | + | 0.250905i | ||||
\(148\) | 13.0147 | + | 9.45572i | 1.06980 | + | 0.777255i | ||||
\(149\) | −7.84361 | − | 5.69872i | −0.642573 | − | 0.466857i | 0.218160 | − | 0.975913i | \(-0.429995\pi\) |
−0.860733 | + | 0.509056i | \(0.829995\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.68515 | + | 14.4194i | 0.381272 | + | 1.17343i | 0.939149 | + | 0.343511i | \(0.111616\pi\) |
−0.557877 | + | 0.829924i | \(0.688384\pi\) | |||||||
\(152\) | −0.0574342 | + | 0.0417284i | −0.00465853 | + | 0.00338462i | ||||
\(153\) | 0.0882264 | 0.00713268 | ||||||||
\(154\) | 1.28307 | + | 2.46489i | 0.103393 | + | 0.198627i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.74921 | + | 1.27088i | −0.140049 | + | 0.101752i | ||||
\(157\) | 4.59834 | + | 14.1522i | 0.366987 | + | 1.12947i | 0.948727 | + | 0.316096i | \(0.102372\pi\) |
−0.581740 | + | 0.813375i | \(0.697628\pi\) | |||||||
\(158\) | 0.0641570 | − | 0.197455i | 0.00510405 | − | 0.0157087i | ||||
\(159\) | −0.705768 | − | 0.512771i | −0.0559710 | − | 0.0406653i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.56702 | + | 20.2112i | −0.517554 | + | 1.59287i | ||||
\(162\) | 0.0810736 | + | 0.249519i | 0.00636974 | + | 0.0196041i | ||||
\(163\) | 2.75158 | − | 1.99914i | 0.215521 | − | 0.156585i | −0.474787 | − | 0.880101i | \(-0.657475\pi\) |
0.690308 | + | 0.723516i | \(0.257475\pi\) | |||||||
\(164\) | 22.5283 | 1.75917 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.0648629 | −0.00503434 | ||||||||
\(167\) | −18.2970 | + | 13.2936i | −1.41587 | + | 1.02869i | −0.423429 | + | 0.905929i | \(0.639174\pi\) |
−0.992437 | + | 0.122757i | \(0.960826\pi\) | |||||||
\(168\) | 1.01782 | + | 3.13253i | 0.0785266 | + | 0.241680i | ||||
\(169\) | −3.62986 | + | 11.1716i | −0.279220 | + | 0.859351i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0556868 | + | 0.0404588i | 0.00425847 | + | 0.00309396i | ||||
\(172\) | −7.05478 | + | 21.7124i | −0.537922 | + | 1.65555i | ||||
\(173\) | 4.04543 | + | 12.4506i | 0.307568 | + | 0.946598i | 0.978706 | + | 0.205266i | \(0.0658058\pi\) |
−0.671138 | + | 0.741333i | \(0.734194\pi\) | |||||||
\(174\) | 0.792943 | − | 0.576107i | 0.0601128 | − | 0.0436745i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −10.6607 | − | 5.31556i | −0.803584 | − | 0.400675i | ||||
\(177\) | −1.83604 | −0.138005 | ||||||||
\(178\) | 3.09439 | − | 2.24821i | 0.231935 | − | 0.168510i | ||||
\(179\) | −4.69008 | − | 14.4346i | −0.350553 | − | 1.07889i | −0.958543 | − | 0.284947i | \(-0.908024\pi\) |
0.607990 | − | 0.793944i | \(-0.291976\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.14353 | − | 0.830823i | −0.0849978 | − | 0.0617546i | 0.544475 | − | 0.838777i | \(-0.316729\pi\) |
−0.629473 | + | 0.777023i | \(0.716729\pi\) | |||||||
\(182\) | −0.758911 | − | 0.551381i | −0.0562542 | − | 0.0408711i | ||||
\(183\) | 3.10875 | − | 9.56775i | 0.229805 | − | 0.707268i | ||||
\(184\) | 2.12088 | + | 6.52740i | 0.156354 | + | 0.481207i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.51468 | 0.184385 | ||||||||
\(187\) | −0.261867 | − | 0.130570i | −0.0191496 | − | 0.00954820i | ||||
\(188\) | 1.75354 | 0.127890 | ||||||||
\(189\) | 2.58362 | − | 1.87711i | 0.187931 | − | 0.136540i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.51701 | − | 4.66887i | 0.109767 | − | 0.337827i | −0.881053 | − | 0.473018i | \(-0.843165\pi\) |
0.990820 | + | 0.135190i | \(0.0431646\pi\) | |||||||
\(192\) | −5.17372 | − | 3.75893i | −0.373381 | − | 0.271277i | ||||
\(193\) | 7.86354 | + | 5.71320i | 0.566030 | + | 0.411245i | 0.833661 | − | 0.552276i | \(-0.186241\pi\) |
−0.267631 | + | 0.963522i | \(0.586241\pi\) | |||||||
\(194\) | 0.331752 | − | 1.02103i | 0.0238184 | − | 0.0733054i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.99735 | − | 3.63079i | 0.356953 | − | 0.259342i | ||||
\(197\) | 8.88764 | 0.633218 | 0.316609 | − | 0.948556i | \(-0.397456\pi\) | ||||
0.316609 | + | 0.948556i | \(0.397456\pi\) | |||||||
\(198\) | 0.128636 | − | 0.860588i | 0.00914175 | − | 0.0611593i | ||||
\(199\) | 18.0381 | 1.27869 | 0.639343 | − | 0.768921i | \(-0.279206\pi\) | ||||
0.639343 | + | 0.768921i | \(0.279206\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.94776 | + | 9.07228i | 0.207919 | + | 0.639909i | ||||
\(202\) | 0.347945 | − | 1.07086i | 0.0244813 | − | 0.0753457i | ||||
\(203\) | −9.65196 | − | 7.01256i | −0.677435 | − | 0.492185i | ||||
\(204\) | −0.137840 | − | 0.100147i | −0.00965075 | − | 0.00701168i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.169671 | − | 0.522194i | −0.0118216 | − | 0.0363830i | ||||
\(207\) | 5.38361 | − | 3.91142i | 0.374186 | − | 0.271862i | ||||
\(208\) | 4.02134 | 0.278830 | ||||||||
\(209\) | −0.105409 | − | 0.202500i | −0.00729128 | − | 0.0140072i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.5444 | + | 10.5671i | −1.00127 | + | 0.727469i | −0.962361 | − | 0.271774i | \(-0.912390\pi\) |
−0.0389136 | + | 0.999243i | \(0.512390\pi\) | |||||||
\(212\) | 0.520603 | + | 1.60225i | 0.0357552 | + | 0.110043i | ||||
\(213\) | 1.44142 | − | 4.43625i | 0.0987647 | − | 0.303967i | ||||
\(214\) | −3.34106 | − | 2.42743i | −0.228390 | − | 0.165935i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.318714 | − | 0.980901i | 0.0216857 | − | 0.0667418i | ||||
\(217\) | −9.45884 | − | 29.1113i | −0.642108 | − | 1.97621i | ||||
\(218\) | 0.877182 | − | 0.637310i | 0.0594103 | − | 0.0431641i | ||||
\(219\) | −7.16034 | −0.483851 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.0987789 | 0.00664459 | ||||||||
\(222\) | 1.76812 | − | 1.28461i | 0.118668 | − | 0.0862174i | ||||
\(223\) | 4.24865 | + | 13.0760i | 0.284511 | + | 0.875635i | 0.986545 | + | 0.163491i | \(0.0522755\pi\) |
−0.702034 | + | 0.712144i | \(0.747724\pi\) | |||||||
\(224\) | 2.96558 | − | 9.12713i | 0.198146 | − | 0.609832i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.91955 | + | 2.12118i | 0.194205 | + | 0.141099i | ||||
\(227\) | −0.204796 | + | 0.630298i | −0.0135928 | + | 0.0418344i | −0.957623 | − | 0.288025i | \(-0.907001\pi\) |
0.944030 | + | 0.329859i | \(0.107001\pi\) | |||||||
\(228\) | −0.0410768 | − | 0.126421i | −0.00272038 | − | 0.00837246i | ||||
\(229\) | 6.05987 | − | 4.40275i | 0.400447 | − | 0.290942i | −0.369276 | − | 0.929320i | \(-0.620394\pi\) |
0.769723 | + | 0.638378i | \(0.220394\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.4465 | + | 1.74790i | −0.687330 | + | 0.115004i | ||||
\(232\) | −3.85306 | −0.252966 | ||||||||
\(233\) | 8.51520 | − | 6.18665i | 0.557849 | − | 0.405301i | −0.272822 | − | 0.962065i | \(-0.587957\pi\) |
0.830671 | + | 0.556763i | \(0.187957\pi\) | |||||||
\(234\) | 0.0907705 | + | 0.279363i | 0.00593385 | + | 0.0182625i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.86854 | + | 2.08411i | 0.186726 | + | 0.135664i | ||||
\(237\) | 0.640209 | + | 0.465139i | 0.0415861 | + | 0.0302140i | ||||
\(238\) | 0.0228428 | − | 0.0703028i | 0.00148068 | − | 0.00455706i | ||||
\(239\) | 5.27684 | + | 16.2404i | 0.341330 | + | 1.05051i | 0.963519 | + | 0.267640i | \(0.0862437\pi\) |
−0.622189 | + | 0.782867i | \(0.713756\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.7082 | −1.07627 | −0.538135 | − | 0.842859i | \(-0.680871\pi\) | ||||
−0.538135 | + | 0.842859i | \(0.680871\pi\) | |||||||
\(242\) | −1.65542 | + | 2.36396i | −0.106415 | + | 0.151961i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −15.7174 | + | 11.4194i | −1.00620 | + | 0.731050i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.945777 | − | 2.91080i | 0.0603006 | − | 0.185586i | ||||
\(247\) | 0.0623472 | + | 0.0452979i | 0.00396706 | + | 0.00288224i | ||||
\(248\) | −7.99763 | − | 5.81062i | −0.507850 | − | 0.368975i | ||||
\(249\) | 0.0763980 | − | 0.235129i | 0.00484152 | − | 0.0149007i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.15646 | − | 3.01984i | 0.262353 | − | 0.190611i | −0.448831 | − | 0.893617i | \(-0.648159\pi\) |
0.711184 | + | 0.703006i | \(0.248159\pi\) | |||||||
\(252\) | −6.16724 | −0.388499 | ||||||||
\(253\) | −21.7679 | + | 3.64219i | −1.36854 | + | 0.228982i | ||||
\(254\) | −2.07259 | −0.130046 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.32908 | + | 10.2458i | 0.208067 | + | 0.640366i | ||||
\(257\) | 1.14282 | − | 3.51724i | 0.0712872 | − | 0.219399i | −0.909065 | − | 0.416654i | \(-0.863203\pi\) |
0.980352 | + | 0.197255i | \(0.0632026\pi\) | |||||||
\(258\) | 2.50920 | + | 1.82304i | 0.156216 | + | 0.113498i | ||||
\(259\) | −21.5221 | − | 15.6367i | −1.33732 | − | 0.971617i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.15444 | + | 3.55299i | 0.0714577 | + | 0.219924i | ||||
\(262\) | 3.47116 | − | 2.52195i | 0.214449 | − | 0.155806i | ||||
\(263\) | −31.6315 | −1.95048 | −0.975241 | − | 0.221147i | \(-0.929020\pi\) | ||||
−0.975241 | + | 0.221147i | \(0.929020\pi\) | |||||||
\(264\) | −2.39766 | + | 2.43976i | −0.147566 | + | 0.150157i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.0466573 | − | 0.0338985i | 0.00286074 | − | 0.00207845i | ||||
\(267\) | 4.50509 | + | 13.8652i | 0.275707 | + | 0.848539i | ||||
\(268\) | 5.69262 | − | 17.5201i | 0.347732 | − | 1.07021i | ||||
\(269\) | 11.9536 | + | 8.68479i | 0.728823 | + | 0.529521i | 0.889191 | − | 0.457536i | \(-0.151268\pi\) |
−0.160368 | + | 0.987057i | \(0.551268\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.05269 | + | 18.6283i | −0.367675 | + | 1.13159i | 0.580614 | + | 0.814179i | \(0.302812\pi\) |
−0.948289 | + | 0.317408i | \(0.897188\pi\) | |||||||
\(272\) | 0.0979234 | + | 0.301377i | 0.00593748 | + | 0.0182737i | ||||
\(273\) | 2.89263 | − | 2.10162i | 0.175070 | − | 0.127196i | ||||
\(274\) | −2.02859 | −0.122551 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −12.8510 | −0.773537 | ||||||||
\(277\) | 20.8001 | − | 15.1122i | 1.24976 | − | 0.908002i | 0.251550 | − | 0.967844i | \(-0.419060\pi\) |
0.998208 | + | 0.0598418i | \(0.0190596\pi\) | |||||||
\(278\) | 1.63659 | + | 5.03691i | 0.0981561 | + | 0.302094i | ||||
\(279\) | −2.96188 | + | 9.11573i | −0.177323 | + | 0.545744i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.6096 | + | 15.7003i | 1.28912 | + | 0.936599i | 0.999787 | − | 0.0206304i | \(-0.00656732\pi\) |
0.289331 | + | 0.957229i | \(0.406567\pi\) | |||||||
\(282\) | 0.0736165 | − | 0.226568i | 0.00438380 | − | 0.0134919i | ||||
\(283\) | −2.23535 | − | 6.87970i | −0.132878 | − | 0.408956i | 0.862376 | − | 0.506268i | \(-0.168975\pi\) |
−0.995254 | + | 0.0973123i | \(0.968975\pi\) | |||||||
\(284\) | −7.28764 | + | 5.29478i | −0.432442 | + | 0.314187i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.144021 | − | 0.963520i | 0.00851616 | − | 0.0569741i | ||||
\(287\) | −37.2546 | −2.19907 | ||||||||
\(288\) | −2.43117 | + | 1.76635i | −0.143258 | + | 0.104083i | ||||
\(289\) | −5.25088 | − | 16.1606i | −0.308876 | − | 0.950621i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.31048 | + | 2.40521i | 0.194064 | + | 0.140996i | ||||
\(292\) | 11.1869 | + | 8.12778i | 0.654666 | + | 0.475643i | ||||
\(293\) | −4.51002 | + | 13.8804i | −0.263478 | + | 0.810902i | 0.728562 | + | 0.684980i | \(0.240189\pi\) |
−0.992040 | + | 0.125922i | \(0.959811\pi\) | |||||||
\(294\) | −0.259323 | − | 0.798115i | −0.0151240 | − | 0.0465470i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.59161 | −0.499377 | ||||||||
\(297\) | 2.96813 | + | 1.47994i | 0.172228 | + | 0.0858747i | ||||
\(298\) | 2.54364 | 0.147349 | ||||||||
\(299\) | 6.02752 | − | 4.37925i | 0.348580 | − | 0.253258i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.6663 | − | 35.9053i | 0.672436 | − | 2.06955i | ||||
\(302\) | −3.21807 | − | 2.33807i | −0.185179 | − | 0.134541i | ||||
\(303\) | 3.47207 | + | 2.52261i | 0.199465 | + | 0.144920i | ||||
\(304\) | −0.0763980 | + | 0.235129i | −0.00438172 | + | 0.0134856i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.0187264 | + | 0.0136055i | −0.00107052 | + | 0.000777775i | ||||
\(307\) | −28.5445 | −1.62912 | −0.814559 | − | 0.580080i | \(-0.803021\pi\) | ||||
−0.814559 | + | 0.580080i | \(0.803021\pi\) | |||||||
\(308\) | 18.3051 | + | 9.12713i | 1.04303 | + | 0.520066i | ||||
\(309\) | 2.09280 | 0.119055 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.07411 | − | 9.46113i | −0.174317 | − | 0.536492i | 0.825285 | − | 0.564717i | \(-0.191015\pi\) |
−0.999602 | + | 0.0282249i | \(0.991015\pi\) | |||||||
\(312\) | 0.356834 | − | 1.09822i | 0.0202018 | − | 0.0621746i | ||||
\(313\) | −13.2929 | − | 9.65786i | −0.751359 | − | 0.545894i | 0.144889 | − | 0.989448i | \(-0.453718\pi\) |
−0.896248 | + | 0.443554i | \(0.853718\pi\) | |||||||
\(314\) | −3.15844 | − | 2.29474i | −0.178241 | − | 0.129500i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.472244 | − | 1.45342i | −0.0265658 | − | 0.0817612i | ||||
\(317\) | 11.4966 | − | 8.35278i | 0.645714 | − | 0.469139i | −0.216094 | − | 0.976373i | \(-0.569332\pi\) |
0.861809 | + | 0.507234i | \(0.169332\pi\) | |||||||
\(318\) | 0.228877 | 0.0128348 | ||||||||
\(319\) | 1.83169 | − | 12.2542i | 0.102555 | − | 0.686104i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.7347 | − | 9.25228i | 0.710780 | − | 0.516412i | ||||
\(322\) | −1.72292 | − | 5.30261i | −0.0960147 | − | 0.295503i | ||||
\(323\) | −0.00187662 | + | 0.00577563i | −0.000104418 | + | 0.000321365i | ||||
\(324\) | 1.56235 | + | 1.13511i | 0.0867971 | + | 0.0630618i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.275743 | + | 0.848650i | −0.0152720 | + | 0.0470024i | ||||
\(327\) | 1.27708 | + | 3.93044i | 0.0706226 | + | 0.217354i | ||||
\(328\) | −9.73387 | + | 7.07207i | −0.537463 | + | 0.390490i | ||||
\(329\) | −2.89979 | −0.159870 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.9119 | −0.599773 | −0.299886 | − | 0.953975i | \(-0.596949\pi\) | ||||
−0.299886 | + | 0.953975i | \(0.596949\pi\) | |||||||
\(332\) | −0.386258 | + | 0.280633i | −0.0211986 | + | 0.0154017i | ||||
\(333\) | 2.57418 | + | 7.92250i | 0.141064 | + | 0.434150i | ||||
\(334\) | 1.83359 | − | 5.64321i | 0.100330 | − | 0.308783i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 9.27969 | + | 6.74209i | 0.506249 | + | 0.367811i | ||||
\(337\) | 1.81890 | − | 5.59800i | 0.0990819 | − | 0.304943i | −0.889214 | − | 0.457491i | \(-0.848748\pi\) |
0.988296 | + | 0.152549i | \(0.0487481\pi\) | |||||||
\(338\) | −0.952330 | − | 2.93097i | −0.0517999 | − | 0.159424i | ||||
\(339\) | −11.1280 | + | 8.08499i | −0.604392 | + | 0.439116i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.2820 | − | 22.6732i | 1.20664 | − | 1.22783i | ||||
\(342\) | −0.0180589 | −0.000976514 | ||||||||
\(343\) | 9.82132 | − | 7.13561i | 0.530302 | − | 0.385287i | ||||
\(344\) | −3.76775 | − | 11.5959i | −0.203144 | − | 0.625212i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.77867 | − | 2.01882i | −0.149382 | − | 0.108533i | ||||
\(347\) | 27.9145 | + | 20.2811i | 1.49853 | + | 1.08875i | 0.970962 | + | 0.239234i | \(0.0768962\pi\) |
0.527569 | + | 0.849512i | \(0.323104\pi\) | |||||||
\(348\) | 2.22941 | − | 6.86141i | 0.119509 | − | 0.367810i | ||||
\(349\) | −1.70378 | − | 5.24371i | −0.0912014 | − | 0.280689i | 0.895044 | − | 0.445978i | \(-0.147144\pi\) |
−0.986245 | + | 0.165289i | \(0.947144\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.11961 | −0.0597602 | ||||||||
\(352\) | 9.83010 | − | 1.64476i | 0.523946 | − | 0.0876662i | ||||
\(353\) | 29.8740 | 1.59003 | 0.795016 | − | 0.606589i | \(-0.207463\pi\) | ||||
0.795016 | + | 0.606589i | \(0.207463\pi\) | |||||||
\(354\) | 0.389706 | − | 0.283138i | 0.0207127 | − | 0.0150486i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8.70008 | − | 26.7761i | 0.461103 | − | 1.41913i | ||||
\(357\) | 0.227943 | + | 0.165611i | 0.0120640 | + | 0.00876504i | ||||
\(358\) | 3.22146 | + | 2.34053i | 0.170259 | + | 0.123701i | ||||
\(359\) | −11.0978 | + | 34.1554i | −0.585717 | + | 1.80265i | 0.0106548 | + | 0.999943i | \(0.496608\pi\) |
−0.596372 | + | 0.802708i | \(0.703392\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.3675 | − | 11.1651i | 0.808815 | − | 0.587639i | ||||
\(362\) | 0.370840 | 0.0194909 | ||||||||
\(363\) | −6.61956 | − | 8.78529i | −0.347437 | − | 0.461108i | ||||
\(364\) | −6.90488 | −0.361914 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.815611 | + | 2.51019i | 0.0426326 | + | 0.131210i | ||||
\(367\) | 2.79069 | − | 8.58887i | 0.145673 | − | 0.448335i | −0.851424 | − | 0.524478i | \(-0.824260\pi\) |
0.997097 | + | 0.0761428i | \(0.0242605\pi\) | |||||||
\(368\) | 19.3365 | + | 14.0488i | 1.00799 | + | 0.732345i | ||||
\(369\) | 9.43772 | + | 6.85690i | 0.491308 | + | 0.356956i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.860909 | − | 2.64961i | −0.0446962 | − | 0.137561i | ||||
\(372\) | 14.9749 | − | 10.8799i | 0.776410 | − | 0.564095i | ||||
\(373\) | −17.1994 | −0.890553 | −0.445277 | − | 0.895393i | \(-0.646895\pi\) | ||||
−0.445277 | + | 0.895393i | \(0.646895\pi\) | |||||||
\(374\) | 0.0757176 | − | 0.0126690i | 0.00391526 | − | 0.000655098i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.757656 | + | 0.550469i | −0.0390731 | + | 0.0283883i | ||||
\(377\) | 1.29251 | + | 3.97795i | 0.0665678 | + | 0.204875i | ||||
\(378\) | −0.258911 | + | 0.796845i | −0.0133169 | + | 0.0409853i | ||||
\(379\) | 6.47382 | + | 4.70350i | 0.332538 | + | 0.241603i | 0.741507 | − | 0.670946i | \(-0.234112\pi\) |
−0.408969 | + | 0.912548i | \(0.634112\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.44117 | − | 7.51314i | 0.125065 | − | 0.384910i | ||||
\(382\) | 0.398002 | + | 1.22492i | 0.0203635 | + | 0.0626725i | ||||
\(383\) | 24.0384 | − | 17.4649i | 1.22831 | − | 0.892417i | 0.231544 | − | 0.972824i | \(-0.425622\pi\) |
0.996762 | + | 0.0804076i | \(0.0256222\pi\) | |||||||
\(384\) | 7.68799 | 0.392326 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.55010 | −0.129797 | ||||||||
\(387\) | −9.56399 | + | 6.94864i | −0.486165 | + | 0.353219i | ||||
\(388\) | −2.44194 | − | 7.51553i | −0.123971 | − | 0.381543i | ||||
\(389\) | −0.183988 | + | 0.566256i | −0.00932855 | + | 0.0287103i | −0.955612 | − | 0.294627i | \(-0.904805\pi\) |
0.946284 | + | 0.323337i | \(0.104805\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.474976 | + | 0.345090i | 0.0240206 | + | 0.0174520i | ||||
\(392\) | −1.01944 | + | 3.13752i | −0.0514897 | + | 0.158469i | ||||
\(393\) | 5.05362 | + | 15.5534i | 0.254922 | + | 0.784568i | ||||
\(394\) | −1.88643 | + | 1.37057i | −0.0950371 | + | 0.0690485i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.95735 | − | 5.68133i | −0.148612 | − | 0.285498i | ||||
\(397\) | −1.66950 | −0.0837898 | −0.0418949 | − | 0.999122i | \(-0.513339\pi\) | ||||
−0.0418949 | + | 0.999122i | \(0.513339\pi\) | |||||||
\(398\) | −3.82865 | + | 2.78168i | −0.191913 | + | 0.139433i | ||||
\(399\) | 0.0679277 | + | 0.209060i | 0.00340064 | + | 0.0104661i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.19771 | + | 6.68253i | 0.459312 | + | 0.333710i | 0.793261 | − | 0.608881i | \(-0.208381\pi\) |
−0.333949 | + | 0.942591i | \(0.608381\pi\) | |||||||
\(402\) | −2.02472 | − | 1.47104i | −0.100984 | − | 0.0733690i | ||||
\(403\) | −3.31614 | + | 10.2060i | −0.165189 | + | 0.508398i | ||||
\(404\) | −2.56114 | − | 7.88237i | −0.127421 | − | 0.392163i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.13008 | 0.155343 | ||||||||
\(407\) | 4.08433 | − | 27.3246i | 0.202453 | − | 1.35443i | ||||
\(408\) | 0.0909950 | 0.00450492 | ||||||||
\(409\) | 6.95565 | − | 5.05358i | 0.343935 | − | 0.249883i | −0.402385 | − | 0.915470i | \(-0.631819\pi\) |
0.746320 | + | 0.665587i | \(0.231819\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.38934 | − | 7.35364i | 0.117858 | − | 0.362728i | ||||
\(412\) | −3.26969 | − | 2.37557i | −0.161086 | − | 0.117036i | ||||
\(413\) | −4.74363 | − | 3.44645i | −0.233419 | − | 0.169589i | ||||
\(414\) | −0.539504 | + | 1.66042i | −0.0265152 | + | 0.0816054i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.72195 | + | 1.97761i | −0.133455 | + | 0.0969604i | ||||
\(417\) | −20.1865 | −0.988536 | ||||||||
\(418\) | 0.0536011 | + | 0.0267261i | 0.00262172 | + | 0.00130721i | ||||
\(419\) | 31.3915 | 1.53358 | 0.766789 | − | 0.641899i | \(-0.221853\pi\) | ||||
0.766789 | + | 0.641899i | \(0.221853\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.41497 | − | 4.35482i | −0.0689613 | − | 0.212241i | 0.910637 | − | 0.413208i | \(-0.135592\pi\) |
−0.979598 | + | 0.200967i | \(0.935592\pi\) | |||||||
\(422\) | 1.45753 | − | 4.48580i | 0.0709513 | − | 0.218366i | ||||
\(423\) | 0.734604 | + | 0.533721i | 0.0357177 | + | 0.0259504i | ||||
\(424\) | −0.727915 | − | 0.528861i | −0.0353507 | − | 0.0256838i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.378171 | + | 1.16389i | 0.0183225 | + | 0.0563908i | ||||
\(427\) | 25.9915 | − | 18.8839i | 1.25782 | − | 0.913858i | ||||
\(428\) | −30.3983 | −1.46936 | ||||||||
\(429\) | 3.32313 | + | 1.65695i | 0.160442 | + | 0.0799982i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.8694 | + | 9.35015i | −0.619896 | + | 0.450381i | −0.852885 | − | 0.522098i | \(-0.825149\pi\) |
0.232989 | + | 0.972479i | \(0.425149\pi\) | |||||||
\(432\) | −1.10991 | − | 3.41595i | −0.0534005 | − | 0.164350i | ||||
\(433\) | −4.88338 | + | 15.0295i | −0.234680 | + | 0.722272i | 0.762483 | + | 0.647008i | \(0.223980\pi\) |
−0.997164 | + | 0.0752639i | \(0.976020\pi\) | |||||||
\(434\) | 6.49696 | + | 4.72032i | 0.311864 | + | 0.226583i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.46625 | − | 7.59034i | 0.118112 | − | 0.363511i | ||||
\(437\) | 0.141544 | + | 0.435628i | 0.00677098 | + | 0.0208389i | ||||
\(438\) | 1.51981 | − | 1.10420i | 0.0726192 | − | 0.0527609i | ||||
\(439\) | 21.5227 | 1.02722 | 0.513611 | − | 0.858023i | \(-0.328307\pi\) | ||||
0.513611 | + | 0.858023i | \(0.328307\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.19862 | 0.152315 | ||||||||
\(442\) | −0.0209662 | + | 0.0152328i | −0.000997258 | + | 0.000724551i | ||||
\(443\) | −3.14484 | − | 9.67881i | −0.149416 | − | 0.459854i | 0.848137 | − | 0.529777i | \(-0.177725\pi\) |
−0.997552 | + | 0.0699233i | \(0.977725\pi\) | |||||||
\(444\) | 4.97116 | − | 15.2997i | 0.235921 | − | 0.726090i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.91826 | − | 2.12024i | −0.138184 | − | 0.100396i | ||||
\(447\) | −2.99599 | + | 9.22071i | −0.141706 | + | 0.436125i | ||||
\(448\) | −6.31100 | − | 19.4233i | −0.298167 | − | 0.917663i | ||||
\(449\) | −31.2352 | + | 22.6937i | −1.47408 | + | 1.07098i | −0.494673 | + | 0.869079i | \(0.664712\pi\) |
−0.979406 | + | 0.201902i | \(0.935288\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.8646 | − | 34.3194i | −0.841209 | − | 1.61604i | ||||
\(452\) | 26.5632 | 1.24943 | ||||||||
\(453\) | 12.2659 | − | 8.91168i | 0.576301 | − | 0.418707i | ||||
\(454\) | −0.0537303 | − | 0.165365i | −0.00252169 | − | 0.00776096i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.0574342 | + | 0.0417284i | 0.00268960 | + | 0.00195411i | ||||
\(457\) | 18.9017 | + | 13.7329i | 0.884183 | + | 0.642396i | 0.934355 | − | 0.356344i | \(-0.115977\pi\) |
−0.0501720 | + | 0.998741i | \(0.515977\pi\) | |||||||
\(458\) | −0.607275 | + | 1.86900i | −0.0283761 | + | 0.0873326i | ||||
\(459\) | −0.0272635 | − | 0.0839083i | −0.00127255 | − | 0.00391651i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.93120 | 0.229669 | 0.114834 | − | 0.993385i | \(-0.463366\pi\) | ||||
0.114834 | + | 0.993385i | \(0.463366\pi\) | |||||||
\(462\) | 1.94776 | − | 1.98197i | 0.0906181 | − | 0.0922094i | ||||
\(463\) | −26.9648 | −1.25316 | −0.626580 | − | 0.779357i | \(-0.715546\pi\) | ||||
−0.626580 | + | 0.779357i | \(0.715546\pi\) | |||||||
\(464\) | −10.8555 | + | 7.88699i | −0.503954 | + | 0.366144i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.853329 | + | 2.62628i | −0.0395297 | + | 0.121660i | ||||
\(467\) | −19.1558 | − | 13.9175i | −0.886423 | − | 0.644024i | 0.0485201 | − | 0.998822i | \(-0.484550\pi\) |
−0.934943 | + | 0.354798i | \(0.884550\pi\) | |||||||
\(468\) | 1.74921 | + | 1.27088i | 0.0808574 | + | 0.0587464i | ||||
\(469\) | −9.41376 | + | 28.9726i | −0.434687 | + | 1.33783i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.0386 | − | 8.74655i | 0.554709 | − | 0.403020i | ||||
\(472\) | −1.89366 | −0.0871627 | ||||||||
\(473\) | 38.6707 | − | 6.47035i | 1.77808 | − | 0.297507i | ||||
\(474\) | −0.207616 | −0.00953613 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.168140 | − | 0.517482i | −0.00770669 | − | 0.0237188i | ||||
\(477\) | −0.269579 | + | 0.829680i | −0.0123432 | + | 0.0379884i | ||||
\(478\) | −3.62449 | − | 2.63334i | −0.165780 | − | 0.120446i | ||||
\(479\) | 10.9412 | + | 7.94922i | 0.499915 | + | 0.363209i | 0.808984 | − | 0.587830i | \(-0.200018\pi\) |
−0.309070 | + | 0.951039i | \(0.600018\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.88206 | + | 8.87008i | 0.131411 | + | 0.404441i | ||||
\(482\) | 3.54637 | − | 2.57659i | 0.161533 | − | 0.117361i | ||||
\(483\) | 21.2513 | 0.966969 | ||||||||
\(484\) | 0.369771 | + | 21.2396i | 0.0168078 | + | 0.965437i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.212253 | − | 0.154211i | 0.00962801 | − | 0.00699516i | ||||
\(487\) | 2.66590 | + | 8.20480i | 0.120803 | + | 0.371795i | 0.993113 | − | 0.117159i | \(-0.0373787\pi\) |
−0.872310 | + | 0.488954i | \(0.837379\pi\) | |||||||
\(488\) | 3.20630 | − | 9.86798i | 0.145142 | − | 0.446703i | ||||
\(489\) | −2.75158 | − | 1.99914i | −0.124431 | − | 0.0904043i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.00565 | + | 24.6388i | −0.361290 | + | 1.11194i | 0.590982 | + | 0.806685i | \(0.298740\pi\) |
−0.952272 | + | 0.305251i | \(0.901260\pi\) | |||||||
\(492\) | −6.96164 | − | 21.4257i | −0.313855 | − | 0.965947i | ||||
\(493\) | −0.266651 | + | 0.193733i | −0.0120094 | + | 0.00872532i | ||||
\(494\) | −0.0202189 | −0.000909690 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −34.4263 | −1.54579 | ||||||||
\(497\) | 12.0514 | − | 8.75585i | 0.540579 | − | 0.392754i | ||||
\(498\) | 0.0200437 | + | 0.0616883i | 0.000898182 | + | 0.00276432i | ||||
\(499\) | −8.66717 | + | 26.6748i | −0.387996 | + | 1.19413i | 0.546288 | + | 0.837597i | \(0.316040\pi\) |
−0.934284 | + | 0.356531i | \(0.883960\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.2970 | + | 13.2936i | 0.817450 | + | 0.593913i | ||||
\(502\) | −0.416529 | + | 1.28194i | −0.0185906 | + | 0.0572160i | ||||
\(503\) | −9.08507 | − | 27.9610i | −0.405083 | − | 1.24672i | −0.920826 | − | 0.389974i | \(-0.872484\pi\) |
0.515743 | − | 0.856744i | \(-0.327516\pi\) | |||||||
\(504\) | 2.66469 | − | 1.93601i | 0.118695 | − | 0.0862368i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.05864 | − | 4.12992i | 0.180429 | − | 0.183597i | ||||
\(507\) | 11.7465 | 0.521680 | ||||||||
\(508\) | −12.3422 | + | 8.96714i | −0.547597 | + | 0.397853i | ||||
\(509\) | −5.99195 | − | 18.4413i | −0.265589 | − | 0.817398i | −0.991557 | − | 0.129670i | \(-0.958608\pi\) |
0.725969 | − | 0.687728i | \(-0.241392\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.4996 | − | 13.4407i | −0.818373 | − | 0.594583i | ||||
\(512\) | −14.7261 | − | 10.6991i | −0.650806 | − | 0.472838i | ||||
\(513\) | 0.0212704 | − | 0.0654637i | 0.000939113 | − | 0.00289029i | ||||
\(514\) | 0.299830 | + | 0.922782i | 0.0132249 | + | 0.0407022i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 22.8298 | 1.00502 | ||||||||
\(517\) | −1.39052 | − | 2.67132i | −0.0611552 | − | 0.117485i | ||||
\(518\) | 6.97949 | 0.306661 | ||||||||
\(519\) | 10.5911 | − | 7.69487i | 0.464897 | − | 0.337767i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.72734 | − | 23.7823i | 0.338541 | − | 1.04192i | −0.626410 | − | 0.779493i | \(-0.715477\pi\) |
0.964951 | − | 0.262429i | \(-0.0845235\pi\) | |||||||
\(522\) | −0.792943 | − | 0.576107i | −0.0347062 | − | 0.0252155i | ||||
\(523\) | −1.76982 | − | 1.28585i | −0.0773887 | − | 0.0562262i | 0.548418 | − | 0.836204i | \(-0.315230\pi\) |
−0.625807 | + | 0.779978i | \(0.715230\pi\) | |||||||
\(524\) | 9.75939 | − | 30.0363i | 0.426341 | − | 1.31214i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.71389 | − | 4.87793i | 0.292740 | − | 0.212688i | ||||
\(527\) | −0.845637 | −0.0368365 | ||||||||
\(528\) | −1.76104 | + | 11.7816i | −0.0766395 | + | 0.512727i | ||||
\(529\) | 21.2824 | 0.925322 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.567369 | + | 1.74618i | 0.0246217 | + | 0.0757778i | ||||
\(532\) | 0.131180 | − | 0.403730i | 0.00568737 | − | 0.0175039i | ||||
\(533\) | 10.5665 | + | 7.67703i | 0.457687 | + | 0.332529i | ||||
\(534\) | −3.09439 | − | 2.24821i | −0.133908 | − | 0.0972895i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.04026 | + | 9.35697i | 0.131319 | + | 0.404159i | ||||
\(537\) | −12.2788 | + | 8.92106i | −0.529869 | + | 0.384972i | ||||
\(538\) | −3.87648 | −0.167127 | ||||||||
\(539\) | −9.49390 | − | 4.73375i | −0.408931 | − | 0.203897i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.9689 | + | 7.96939i | −0.471591 | + | 0.342631i | −0.798061 | − | 0.602577i | \(-0.794141\pi\) |
0.326470 | + | 0.945208i | \(0.394141\pi\) | |||||||
\(542\) | −1.58798 | − | 4.88731i | −0.0682097 | − | 0.209928i | ||||
\(543\) | −0.436789 | + | 1.34430i | −0.0187444 | + | 0.0576894i | ||||
\(544\) | −0.214493 | − | 0.155838i | −0.00919632 | − | 0.00668152i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.289878 | + | 0.892153i | −0.0124056 | + | 0.0381806i | ||||
\(547\) | 1.14732 | + | 3.53110i | 0.0490560 | + | 0.150979i | 0.972584 | − | 0.232553i | \(-0.0747078\pi\) |
−0.923528 | + | 0.383531i | \(0.874708\pi\) | |||||||
\(548\) | −12.0802 | + | 8.77677i | −0.516040 | + | 0.374925i | ||||
\(549\) | −10.0601 | −0.429356 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.257147 | −0.0109548 | ||||||||
\(552\) | 5.55254 | − | 4.03416i | 0.236332 | − | 0.171705i | ||||
\(553\) | 0.780939 | + | 2.40348i | 0.0332089 | + | 0.102207i | ||||
\(554\) | −2.08443 | + | 6.41522i | −0.0885590 | + | 0.272557i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 31.5383 | + | 22.9139i | 1.33752 | + | 0.971766i | ||||
\(557\) | −2.03185 | + | 6.25339i | −0.0860922 | + | 0.264964i | −0.984830 | − | 0.173522i | \(-0.944485\pi\) |
0.898738 | + | 0.438486i | \(0.144485\pi\) | |||||||
\(558\) | −0.777078 | − | 2.39160i | −0.0328963 | − | 0.101244i | ||||
\(559\) | −10.7079 | + | 7.77974i | −0.452896 | + | 0.329048i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.0432577 | + | 0.289399i | −0.00182634 | + | 0.0122184i | ||||
\(562\) | −7.00786 | −0.295609 | ||||||||
\(563\) | −5.58931 | + | 4.06087i | −0.235561 | + | 0.171145i | −0.699303 | − | 0.714825i | \(-0.746506\pi\) |
0.463742 | + | 0.885970i | \(0.346506\pi\) | |||||||
\(564\) | −0.541873 | − | 1.66771i | −0.0228170 | − | 0.0702235i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.53539 | + | 1.11552i | 0.0645372 | + | 0.0468890i | ||||
\(567\) | −2.58362 | − | 1.87711i | −0.108502 | − | 0.0788311i | ||||
\(568\) | 1.48666 | − | 4.57545i | 0.0623787 | − | 0.191982i | ||||
\(569\) | −2.08515 | − | 6.41743i | −0.0874140 | − | 0.269033i | 0.897789 | − | 0.440427i | \(-0.145173\pi\) |
−0.985203 | + | 0.171394i | \(0.945173\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.68928 | 0.405484 | 0.202742 | − | 0.979232i | \(-0.435015\pi\) | ||||
0.202742 | + | 0.979232i | \(0.435015\pi\) | |||||||
\(572\) | −3.31107 | − | 6.36086i | −0.138443 | − | 0.265961i | ||||
\(573\) | −4.90914 | −0.205082 | ||||||||
\(574\) | 7.90742 | − | 5.74508i | 0.330049 | − | 0.239795i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.97619 | + | 6.08207i | −0.0823411 | + | 0.253420i | ||||
\(577\) | 12.2565 | + | 8.90484i | 0.510243 | + | 0.370713i | 0.812916 | − | 0.582381i | \(-0.197879\pi\) |
−0.302673 | + | 0.953095i | \(0.597879\pi\) | |||||||
\(578\) | 3.60666 | + | 2.62039i | 0.150017 | + | 0.108994i | ||||
\(579\) | 3.00361 | − | 9.24415i | 0.124826 | − | 0.384174i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.638745 | − | 0.464076i | 0.0264996 | − | 0.0192531i | ||||
\(582\) | −1.07357 | −0.0445009 | ||||||||
\(583\) | 2.02802 | − | 2.06364i | 0.0839921 | − | 0.0854671i | ||||
\(584\) | −7.38503 | −0.305595 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.18325 | − | 3.64166i | −0.0488795 | − | 0.150436i | ||||
\(587\) | 8.34693 | − | 25.6892i | 0.344514 | − | 1.06031i | −0.617329 | − | 0.786705i | \(-0.711785\pi\) |
0.961843 | − | 0.273601i | \(-0.0882149\pi\) | |||||||
\(588\) | −4.99735 | − | 3.63079i | −0.206087 | − | 0.149731i | ||||
\(589\) | −0.533749 | − | 0.387791i | −0.0219927 | − | 0.0159787i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.74643 | − | 8.45265i | −0.112973 | − | 0.347696i | ||||
\(592\) | −24.2058 | + | 17.5865i | −0.994850 | + | 0.722801i | ||||
\(593\) | 22.1863 | 0.911084 | 0.455542 | − | 0.890214i | \(-0.349446\pi\) | ||||
0.455542 | + | 0.890214i | \(0.349446\pi\) | |||||||
\(594\) | −0.858218 | + | 0.143596i | −0.0352131 | + | 0.00589183i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.1473 | − | 11.0052i | 0.620458 | − | 0.450789i | ||||
\(597\) | −5.57408 | − | 17.1552i | −0.228132 | − | 0.702118i | ||||
\(598\) | −0.604033 | + | 1.85902i | −0.0247007 | + | 0.0760210i | ||||
\(599\) | −9.50487 | − | 6.90569i | −0.388359 | − | 0.282159i | 0.376424 | − | 0.926448i | \(-0.377154\pi\) |
−0.764783 | + | 0.644289i | \(0.777154\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.6242 | − | 32.6979i | 0.433370 | − | 1.33378i | −0.461377 | − | 0.887204i | \(-0.652645\pi\) |
0.894747 | − | 0.446572i | \(-0.147355\pi\) | |||||||
\(602\) | 3.06077 | + | 9.42010i | 0.124748 | + | 0.383934i | ||||
\(603\) | 7.71734 | − | 5.60698i | 0.314274 | − | 0.228334i | ||||
\(604\) | −29.2793 | −1.19136 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.12597 | −0.0457395 | ||||||||
\(607\) | 11.0267 | − | 8.01137i | 0.447560 | − | 0.325172i | −0.341071 | − | 0.940037i | \(-0.610790\pi\) |
0.788632 | + | 0.614866i | \(0.210790\pi\) | |||||||
\(608\) | −0.0639196 | − | 0.196724i | −0.00259228 | − | 0.00797822i | ||||
\(609\) | −3.68672 | + | 11.3466i | −0.149393 | + | 0.459786i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.822467 | + | 0.597557i | 0.0332735 | + | 0.0241746i | ||||
\(612\) | −0.0526503 | + | 0.162041i | −0.00212826 | + | 0.00655012i | ||||
\(613\) | 2.11057 | + | 6.49565i | 0.0852450 | + | 0.262357i | 0.984589 | − | 0.174885i | \(-0.0559553\pi\) |
−0.899344 | + | 0.437242i | \(0.855955\pi\) | |||||||
\(614\) | 6.05866 | − | 4.40187i | 0.244508 | − | 0.177645i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.7743 | + | 1.80275i | −0.434110 | + | 0.0726349i | ||||
\(617\) | −30.3730 | −1.22277 | −0.611386 | − | 0.791333i | \(-0.709388\pi\) | ||||
−0.611386 | + | 0.791333i | \(0.709388\pi\) | |||||||
\(618\) | −0.444205 | + | 0.322734i | −0.0178685 | + | 0.0129823i | ||||
\(619\) | −7.96890 | − | 24.5258i | −0.320297 | − | 0.985773i | −0.973519 | − | 0.228607i | \(-0.926583\pi\) |
0.653222 | − | 0.757167i | \(-0.273417\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.38361 | − | 3.91142i | −0.216037 | − | 0.156960i | ||||
\(622\) | 2.11150 | + | 1.53410i | 0.0846635 | + | 0.0615117i | ||||
\(623\) | −14.3871 | + | 44.2790i | −0.576408 | + | 1.77400i | ||||
\(624\) | −1.24266 | − | 3.82452i | −0.0497463 | − | 0.153103i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.31081 | 0.172295 | ||||||||
\(627\) | −0.160016 | + | 0.162826i | −0.00639041 | + | 0.00650263i | ||||
\(628\) | −28.7368 | −1.14672 | ||||||||
\(629\) | −0.594583 | + | 0.431990i | −0.0237076 | + | 0.0172246i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.90021 | + | 24.3143i | −0.314502 | + | 0.967939i | 0.661456 | + | 0.749984i | \(0.269939\pi\) |
−0.975959 | + | 0.217955i | \(0.930061\pi\) | |||||||
\(632\) | 0.660299 | + | 0.479735i | 0.0262653 | + | 0.0190828i | ||||
\(633\) | 14.5444 | + | 10.5671i | 0.578086 | + | 0.420004i | ||||
\(634\) | −1.15210 | + | 3.54581i | −0.0457559 | + | 0.140822i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.36296 | − | 0.990246i | 0.0540447 | − | 0.0392658i | ||||
\(637\) | 3.58119 | 0.141892 | ||||||||
\(638\) | 1.50095 | + | 2.88347i | 0.0594233 | + | 0.114157i | ||||
\(639\) | −4.66454 | −0.184527 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.25851 | − | 3.87329i | −0.0497081 | − | 0.152986i | 0.923121 | − | 0.384509i | \(-0.125629\pi\) |
−0.972829 | + | 0.231523i | \(0.925629\pi\) | |||||||
\(642\) | −1.27617 | + | 3.92766i | −0.0503665 | + | 0.155012i | ||||
\(643\) | 9.16601 | + | 6.65950i | 0.361472 | + | 0.262625i | 0.753666 | − | 0.657258i | \(-0.228284\pi\) |
−0.392194 | + | 0.919883i | \(0.628284\pi\) | |||||||
\(644\) | −33.2020 | − | 24.1226i | −1.30834 | − | 0.950565i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.000492348 | − | 0.00151529i | −1.93712e−5 | − | 5.96184e-5i | ||||
\(647\) | −29.8107 | + | 21.6587i | −1.17198 | + | 0.851492i | −0.991244 | − | 0.132040i | \(-0.957847\pi\) |
−0.180734 | + | 0.983532i | \(0.557847\pi\) | |||||||
\(648\) | −1.03138 | −0.0405164 | ||||||||
\(649\) | 0.900218 | − | 6.02256i | 0.0353366 | − | 0.236406i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −24.7636 | + | 17.9918i | −0.970561 | + | 0.705154i | ||||
\(652\) | 2.02968 | + | 6.24671i | 0.0794883 | + | 0.244640i | ||||
\(653\) | −4.72079 | + | 14.5291i | −0.184739 | + | 0.568568i | −0.999944 | − | 0.0106050i | \(-0.996624\pi\) |
0.815205 | + | 0.579173i | \(0.196624\pi\) | |||||||
\(654\) | −0.877182 | − | 0.637310i | −0.0343005 | − | 0.0249208i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −12.9478 | + | 39.8493i | −0.505528 | + | 1.55585i | ||||
\(657\) | 2.21267 | + | 6.80989i | 0.0863243 | + | 0.265679i | ||||
\(658\) | 0.615490 | − | 0.447180i | 0.0239943 | − | 0.0174329i | ||||
\(659\) | 11.8996 | 0.463544 | 0.231772 | − | 0.972770i | \(-0.425548\pi\) | ||||
0.231772 | + | 0.972770i | \(0.425548\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.8648 | −1.74504 | −0.872520 | − | 0.488578i | \(-0.837516\pi\) | ||||
−0.872520 | + | 0.488578i | \(0.837516\pi\) | |||||||
\(662\) | 2.31609 | − | 1.68274i | 0.0900174 | − | 0.0654015i | ||||
\(663\) | −0.0305244 | − | 0.0939443i | −0.00118547 | − | 0.00364849i | ||||
\(664\) | 0.0787953 | − | 0.242507i | 0.00305785 | − | 0.00941110i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.76812 | − | 1.28461i | −0.0685131 | − | 0.0497777i | ||||
\(667\) | −7.68219 | + | 23.6434i | −0.297456 | + | 0.915474i | ||||
\(668\) | −13.4966 | − | 41.5383i | −0.522200 | − | 1.60717i | ||||
\(669\) | 11.1231 | − | 8.08142i | 0.430045 | − | 0.312446i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.8597 | + | 14.8884i | 1.15272 | + | 0.574759i | ||||
\(672\) | −9.59683 | −0.370206 | ||||||||
\(673\) | −15.4576 | + | 11.2306i | −0.595848 | + | 0.432909i | −0.844403 | − | 0.535709i | \(-0.820044\pi\) |
0.248555 | + | 0.968618i | \(0.420044\pi\) | |||||||
\(674\) | 0.477207 | + | 1.46869i | 0.0183813 | + | 0.0565719i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −18.3521 | − | 13.3336i | −0.705849 | − | 0.512830i | ||||
\(677\) | 37.5881 | + | 27.3093i | 1.44463 | + | 1.04958i | 0.987050 | + | 0.160414i | \(0.0512829\pi\) |
0.457578 | + | 0.889170i | \(0.348717\pi\) | |||||||
\(678\) | 1.11517 | − | 3.43213i | 0.0428278 | − | 0.131810i | ||||
\(679\) | 4.03819 | + | 12.4283i | 0.154971 | + | 0.476953i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.662735 | 0.0253961 | ||||||||
\(682\) | −1.23295 | + | 8.24860i | −0.0472122 | + | 0.315855i | ||||
\(683\) | 42.5651 | 1.62871 | 0.814355 | − | 0.580367i | \(-0.197091\pi\) | ||||
0.814355 | + | 0.580367i | \(0.197091\pi\) | |||||||
\(684\) | −0.107540 | + | 0.0781327i | −0.00411191 | + | 0.00298748i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.984219 | + | 3.02912i | −0.0375777 | + | 0.115652i | ||||
\(687\) | −6.05987 | − | 4.40275i | −0.231198 | − | 0.167976i | ||||
\(688\) | −34.3514 | − | 24.9577i | −1.30963 | − | 0.951505i | ||||
\(689\) | −0.301823 | + | 0.928915i | −0.0114985 | + | 0.0353888i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.4249 | + | 20.6519i | −1.08134 | + | 0.785636i | −0.977915 | − | 0.209001i | \(-0.932979\pi\) |
−0.103420 | + | 0.994638i | \(0.532979\pi\) | |||||||
\(692\) | −25.2815 | −0.961057 | ||||||||
\(693\) | 4.89050 | + | 9.39509i | 0.185775 | + | 0.356890i | ||||
\(694\) | −9.05253 | −0.343629 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.19066 | + | 3.66448i | 0.0451319 | + | 0.138902i | ||||
\(697\) | −0.318046 | + | 0.978846i | −0.0120469 | + | 0.0370764i | ||||
\(698\) | 1.17027 | + | 0.850252i | 0.0442954 | + | 0.0321825i | ||||
\(699\) | −8.51520 | − | 6.18665i | −0.322074 | − | 0.234001i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.47794 | − | 29.1701i | −0.357977 | − | 1.10174i | −0.954263 | − | 0.298968i | \(-0.903358\pi\) |
0.596286 | − | 0.802772i | \(-0.296642\pi\) | |||||||
\(702\) | 0.237640 | − | 0.172656i | 0.00896916 | − | 0.00651647i | ||||
\(703\) | −0.573390 | −0.0216258 | ||||||||
\(704\) | 14.8667 | − | 15.1277i | 0.560309 | − | 0.570148i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.34086 | + | 4.60690i | −0.238641 | + | 0.173383i | ||||
\(707\) | 4.23530 | + | 13.0349i | 0.159285 | + | 0.490228i | ||||
\(708\) | 1.09568 | − | 3.37217i | 0.0411783 | − | 0.126734i | ||||
\(709\) | −12.2100 | − | 8.87107i | −0.458555 | − | 0.333160i | 0.334409 | − | 0.942428i | \(-0.391463\pi\) |
−0.792964 | + | 0.609268i | \(0.791463\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.244538 | − | 0.752611i | 0.00917090 | − | 0.0282251i | ||||
\(712\) | 4.64646 | + | 14.3003i | 0.174133 | + | 0.535927i | ||||
\(713\) | −51.6010 | + | 37.4903i | −1.93247 | + | 1.40402i | ||||
\(714\) | −0.0739208 | −0.00276642 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 29.3101 | 1.09537 | ||||||||
\(717\) | 13.8149 | − | 10.0371i | 0.515929 | − | 0.374844i | ||||
\(718\) | −2.91160 | − | 8.96099i | −0.108660 | − | 0.334421i | ||||
\(719\) | −1.91288 | + | 5.88723i | −0.0713383 | + | 0.219557i | −0.980369 | − | 0.197173i | \(-0.936824\pi\) |
0.909030 | + | 0.416730i | \(0.136824\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.40701 | + | 3.92842i | 0.201367 | + | 0.146302i | ||||
\(722\) | −1.54001 | + | 4.73968i | −0.0573134 | + | 0.176393i | ||||
\(723\) | 5.16312 | + | 15.8904i | 0.192018 | + | 0.590972i | ||||
\(724\) | 2.20835 | − | 1.60446i | 0.0820725 | − | 0.0596292i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.75982 | + | 0.843898i | 0.102426 | + | 0.0313200i | ||||
\(727\) | 18.1515 | 0.673200 | 0.336600 | − | 0.941648i | \(-0.390723\pi\) | ||||
0.336600 | + | 0.941648i | \(0.390723\pi\) | |||||||
\(728\) | 2.98341 | − | 2.16757i | 0.110572 | − | 0.0803355i | ||||
\(729\) | 0.309017 | + | 0.951057i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.843796 | − | 0.613054i | −0.0312089 | − | 0.0226746i | ||||
\(732\) | 15.7174 | + | 11.4194i | 0.580932 | + | 0.422072i | ||||
\(733\) | 8.88142 | − | 27.3342i | 0.328043 | − | 1.00961i | −0.642005 | − | 0.766700i | \(-0.721897\pi\) |
0.970048 | − | 0.242912i | \(-0.0781027\pi\) | |||||||
\(734\) | 0.732165 | + | 2.25337i | 0.0270247 | + | 0.0831735i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −19.9974 | −0.737113 | ||||||||
\(737\) | −31.2040 | + | 5.22103i | −1.14942 | + | 0.192319i | ||||
\(738\) | −3.06060 | −0.112662 | ||||||||
\(739\) | 37.8896 | − | 27.5284i | 1.39379 | − | 1.01265i | 0.398354 | − | 0.917232i | \(-0.369581\pi\) |
0.995437 | − | 0.0954172i | \(-0.0304185\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0238145 | − | 0.0732936i | 0.000874848 | − | 0.00269251i | ||||
\(742\) | 0.591330 | + | 0.429626i | 0.0217084 | + | 0.0157721i | ||||
\(743\) | 21.5286 | + | 15.6414i | 0.789806 | + | 0.573828i | 0.907906 | − | 0.419174i | \(-0.137680\pi\) |
−0.118100 | + | 0.993002i | \(0.537680\pi\) | |||||||
\(744\) | −3.05482 | + | 9.40178i | −0.111995 | + | 0.344686i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.65064 | − | 2.65235i | 0.133659 | − | 0.0971093i | ||||
\(747\) | −0.247229 | −0.00904564 | ||||||||
\(748\) | 0.396084 | − | 0.403039i | 0.0144823 | − | 0.0147366i | ||||
\(749\) | 50.2691 | 1.83679 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.5406 | + | 38.5959i | 0.457612 | + | 1.40838i | 0.868041 | + | 0.496492i | \(0.165379\pi\) |
−0.410430 | + | 0.911892i | \(0.634621\pi\) | |||||||
\(752\) | −1.00782 | + | 3.10175i | −0.0367514 | + | 0.113109i | ||||
\(753\) | −4.15646 | − | 3.01984i | −0.151470 | − | 0.110049i | ||||
\(754\) | −0.887784 | − | 0.645013i | −0.0323312 | − | 0.0234900i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.90578 | + | 5.86539i | 0.0693126 | + | 0.213322i | ||||
\(757\) | 26.4693 | − | 19.2311i | 0.962045 | − | 0.698966i | 0.00841989 | − | 0.999965i | \(-0.497320\pi\) |
0.953625 | + | 0.300998i | \(0.0973198\pi\) | |||||||
\(758\) | −2.09942 | −0.0762545 | ||||||||
\(759\) | 10.1906 | + | 19.5770i | 0.369894 | + | 0.710600i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.12721 | − | 1.54551i | 0.0771113 | − | 0.0560246i | −0.548562 | − | 0.836110i | \(-0.684824\pi\) |
0.625673 | + | 0.780085i | \(0.284824\pi\) | |||||||
\(762\) | 0.640464 | + | 1.97115i | 0.0232016 | + | 0.0714071i | ||||
\(763\) | −4.07838 | + | 12.5520i | −0.147647 | + | 0.454412i | ||||
\(764\) | 7.66978 | + | 5.57242i | 0.277483 | + | 0.201603i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.40895 | + | 7.41399i | −0.0870389 | + | 0.267878i | ||||
\(767\) | 0.635229 | + | 1.95503i | 0.0229368 | + | 0.0705922i | ||||
\(768\) | 8.71564 | − | 6.33228i | 0.314499 | − | 0.228497i | ||||
\(769\) | 3.23559 | 0.116678 | 0.0583392 | − | 0.998297i | \(-0.481419\pi\) | ||||
0.0583392 | + | 0.998297i | \(0.481419\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.69824 | −0.133189 | ||||||||
\(772\) | −15.1858 | + | 11.0331i | −0.546550 | + | 0.397092i | ||||
\(773\) | −13.4844 | − | 41.5008i | −0.485001 | − | 1.49268i | −0.831980 | − | 0.554806i | \(-0.812792\pi\) |
0.346979 | − | 0.937873i | \(-0.387208\pi\) | |||||||
\(774\) | 0.958431 | − | 2.94975i | 0.0344501 | − | 0.106026i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.41436 | + | 2.48068i | 0.122569 | + | 0.0890512i | ||||
\(777\) | −8.22070 | + | 25.3007i | −0.294916 | + | 0.907658i | ||||
\(778\) | −0.0482710 | − | 0.148563i | −0.00173060 | − | 0.00532623i | ||||
\(779\) | −0.649623 | + | 0.471979i | −0.0232752 | + | 0.0169104i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.8450 | + | 6.90324i | 0.495412 | + | 0.247017i | ||||
\(782\) | −0.154032 | −0.00550818 | ||||||||
\(783\) | 3.02235 | − | 2.19587i | 0.108010 | − | 0.0784739i | ||||
\(784\) | 3.55017 | + | 10.9263i | 0.126792 | + | 0.390225i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.47116 | − | 2.52195i | −0.123812 | − | 0.0899549i | ||||
\(787\) | −3.69251 | − | 2.68277i | −0.131624 | − | 0.0956304i | 0.520025 | − | 0.854151i | \(-0.325923\pi\) |
−0.651649 | + | 0.758521i | \(0.725923\pi\) | |||||||
\(788\) | −5.30382 | + | 16.3235i | −0.188941 | + | 0.581500i | ||||
\(789\) | 9.77467 | + | 30.0833i | 0.347987 | + | 1.07100i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −43.9270 | −1.56186 | ||||||||
\(792\) | 3.06127 | + | 1.52638i | 0.108777 | + | 0.0542375i | ||||
\(793\) | −11.2634 | −0.399974 | ||||||||
\(794\) | 0.354357 | − | 0.257455i | 0.0125757 | − | 0.00913675i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.7645 | + | 33.1297i | −0.381537 | + | 1.17425i | ||||
\(797\) | −9.04526 | − | 6.57177i | −0.320400 | − | 0.232784i | 0.415946 | − | 0.909389i | \(-0.363450\pi\) |
−0.736346 | + | 0.676605i | \(0.763450\pi\) | |||||||
\(798\) | −0.0466573 | − | 0.0338985i | −0.00165165 | − | 0.00119999i | ||||
\(799\) | −0.0247558 | + | 0.0761905i | −0.000875797 | + | 0.00269543i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.7945 | − | 8.56919i | 0.416737 | − | 0.302777i | ||||
\(802\) | −2.98277 | −0.105325 | ||||||||
\(803\) | 3.51074 | − | 23.4872i | 0.123891 | − | 0.828846i | ||||
\(804\) | −18.4217 | −0.649684 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.870021 | − | 2.67765i | −0.0306452 | − | 0.0943162i | ||||
\(807\) | 4.56586 | − | 14.0523i | 0.160726 | − | 0.494664i | ||||
\(808\) | 3.58102 | + | 2.60176i | 0.125980 | + | 0.0915298i | ||||
\(809\) | 36.8440 | + | 26.7687i | 1.29537 | + | 0.941139i | 0.999899 | − | 0.0142137i | \(-0.00452452\pi\) |
0.295468 | + | 0.955353i | \(0.404525\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.872550 | + | 2.68543i | 0.0306394 | + | 0.0942983i | 0.965207 | − | 0.261488i | \(-0.0842131\pi\) |
−0.934567 | + | 0.355786i | \(0.884213\pi\) | |||||||
\(812\) | 18.6395 | − | 13.5424i | 0.654120 | − | 0.475246i | ||||
\(813\) | 19.5869 | 0.686943 | ||||||||
\(814\) | 3.34685 | + | 6.42959i | 0.117307 | + | 0.225357i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.256367 | − | 0.186261i | 0.00897463 | − | 0.00652045i | ||||
\(817\) | −0.251454 | − | 0.773895i | −0.00879725 | − | 0.0270751i | ||||
\(818\) | −0.697043 | + | 2.14528i | −0.0243715 | + | 0.0750079i | ||||
\(819\) | −2.89263 | − | 2.10162i | −0.101077 | − | 0.0734366i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.23460 | + | 22.2658i | −0.252489 | + | 0.777083i | 0.741825 | + | 0.670594i | \(0.233961\pi\) |
−0.994314 | + | 0.106488i | \(0.966039\pi\) | |||||||
\(822\) | 0.626867 | + | 1.92930i | 0.0218645 | + | 0.0672920i | ||||
\(823\) | 37.2994 | − | 27.0996i | 1.30018 | − | 0.944633i | 0.300218 | − | 0.953870i | \(-0.402940\pi\) |
0.999957 | + | 0.00923747i | \(0.00294042\pi\) | |||||||
\(824\) | 2.15848 | 0.0751941 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.53833 | 0.0535255 | ||||||||
\(827\) | −35.1515 | + | 25.5390i | −1.22234 | + | 0.888079i | −0.996292 | − | 0.0860379i | \(-0.972579\pi\) |
−0.226044 | + | 0.974117i | \(0.572579\pi\) | |||||||
\(828\) | 3.97116 | + | 12.2220i | 0.138007 | + | 0.424743i | ||||
\(829\) | 4.78085 | − | 14.7139i | 0.166046 | − | 0.511036i | −0.833066 | − | 0.553173i | \(-0.813417\pi\) |
0.999112 | + | 0.0421372i | \(0.0134167\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.8001 | − | 15.1122i | −0.721548 | − | 0.524235i | ||||
\(832\) | −2.21255 | + | 6.80953i | −0.0767064 | + | 0.236078i | ||||
\(833\) | 0.0872053 | + | 0.268390i | 0.00302149 | + | 0.00929918i | ||||
\(834\) | 4.28465 | − | 3.11298i | 0.148365 | − | 0.107794i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.434825 | − | 0.0727546i | 0.0150387 | − | 0.00251627i | ||||
\(837\) | 9.58484 | 0.331301 | ||||||||
\(838\) | −6.66296 | + | 4.84093i | −0.230168 | + | 0.167227i | ||||
\(839\) | 9.33790 | + | 28.7391i | 0.322380 | + | 0.992184i | 0.972609 | + | 0.232446i | \(0.0746728\pi\) |
−0.650229 | + | 0.759738i | \(0.725327\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.1705 | + | 8.84239i | 0.419673 | + | 0.304910i | ||||
\(842\) | 0.971894 | + | 0.706122i | 0.0334937 | + | 0.0243346i | ||||
\(843\) | 8.25411 | − | 25.4036i | 0.284287 | − | 0.874945i | ||||
\(844\) | −10.7285 | − | 33.0189i | −0.369290 | − | 1.13656i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.238228 | −0.00819045 | ||||||||
\(847\) | −0.611482 | − | 35.1235i | −0.0210108 | − | 1.20686i | ||||
\(848\) | −3.13335 | −0.107600 | ||||||||
\(849\) | −5.85223 | + | 4.25189i | −0.200848 | + | 0.145925i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.1299 | + | 52.7203i | −0.587204 | + | 1.80723i | ||||
\(852\) | 7.28764 | + | 5.29478i | 0.249670 | + | 0.181396i | ||||
\(853\) | −1.62538 | − | 1.18091i | −0.0556521 | − | 0.0404336i | 0.559611 | − | 0.828755i | \(-0.310950\pi\) |
−0.615263 | + | 0.788322i | \(0.710950\pi\) | |||||||
\(854\) | −2.60467 | + | 8.01636i | −0.0891301 | + | 0.274314i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.1343 | − | 9.54262i | 0.448921 | − | 0.326160i | ||||
\(857\) | 33.6095 | 1.14808 | 0.574039 | − | 0.818828i | \(-0.305376\pi\) | ||||
0.574039 | + | 0.818828i | \(0.305376\pi\) | |||||||
\(858\) | −0.960867 | + | 0.160771i | −0.0328034 | + | 0.00548865i | ||||
\(859\) | −13.7301 | −0.468466 | −0.234233 | − | 0.972180i | \(-0.575258\pi\) | ||||
−0.234233 | + | 0.972180i | \(0.575258\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.5123 | + | 35.4312i | 0.392338 | + | 1.20749i | ||||
\(862\) | 1.28967 | − | 3.96920i | 0.0439264 | − | 0.135192i | ||||
\(863\) | 7.08560 | + | 5.14799i | 0.241197 | + | 0.175240i | 0.701816 | − | 0.712358i | \(-0.252373\pi\) |
−0.460620 | + | 0.887598i | \(0.652373\pi\) | |||||||
\(864\) | 2.43117 | + | 1.76635i | 0.0827100 | + | 0.0600923i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.28120 | − | 3.94314i | −0.0435370 | − | 0.133993i | ||||
\(867\) | −13.7470 | + | 9.98777i | −0.466872 | + | 0.339203i | ||||
\(868\) | 59.1120 | 2.00639 | ||||||||
\(869\) | −1.83964 | + | 1.87194i | −0.0624055 | + | 0.0635014i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.64038 | − | 6.27761i | 0.292768 | − | 0.212709i | ||||
\(872\) | 1.31715 | + | 4.05378i | 0.0446044 | + | 0.137278i | ||||
\(873\) | 1.26449 | − | 3.89170i | 0.0427965 | − | 0.131714i | ||||
\(874\) | −0.0972220 | − | 0.0706359i | −0.00328858 | − | 0.00238930i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.27303 | − | 13.1510i | 0.144372 | − | 0.444332i | ||||
\(877\) | 4.71136 | + | 14.5001i | 0.159091 | + | 0.489633i | 0.998552 | − | 0.0537871i | \(-0.0171292\pi\) |
−0.839461 | + | 0.543420i | \(0.817129\pi\) | |||||||
\(878\) | −4.56827 | + | 3.31904i | −0.154172 | + | 0.112012i | ||||
\(879\) | 14.5947 | 0.492268 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.8486 | −0.533953 | −0.266977 | − | 0.963703i | \(-0.586025\pi\) | ||||
−0.266977 | + | 0.963703i | \(0.586025\pi\) | |||||||
\(882\) | −0.678917 | + | 0.493262i | −0.0228603 | + | 0.0166090i | ||||
\(883\) | 10.1854 | + | 31.3474i | 0.342765 | + | 1.05492i | 0.962769 | + | 0.270324i | \(0.0871308\pi\) |
−0.620004 | + | 0.784598i | \(0.712869\pi\) | |||||||
\(884\) | −0.0589476 | + | 0.181422i | −0.00198262 | + | 0.00610189i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.16008 | + | 1.56939i | 0.0725694 | + | 0.0527247i | ||||
\(887\) | −3.47720 | + | 10.7017i | −0.116753 | + | 0.359328i | −0.992309 | − | 0.123789i | \(-0.960495\pi\) |
0.875556 | + | 0.483117i | \(0.160495\pi\) | |||||||
\(888\) | 2.65495 | + | 8.17111i | 0.0890944 | + | 0.274204i | ||||
\(889\) | 20.4100 | − | 14.8288i | 0.684530 | − | 0.497340i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.490303 | − | 3.28018i | 0.0164258 | − | 0.109890i | ||||
\(892\) | −26.5515 | −0.889010 | ||||||||
\(893\) | −0.0505647 | + | 0.0367374i | −0.00169208 | + | 0.00122937i | ||||
\(894\) | −0.786027 | − | 2.41914i | −0.0262887 | − | 0.0809083i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 19.8628 | + | 14.4312i | 0.663570 | + | 0.482112i | ||||
\(897\) | −6.02752 | − | 4.37925i | −0.201253 | − | 0.146219i | ||||
\(898\) | 3.13015 | − | 9.63362i | 0.104455 | − | 0.321478i | ||||
\(899\) | −11.0651 | − | 34.0548i | −0.369041 | − | 1.13579i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.0769667 | −0.00256413 | ||||||||
\(902\) | 9.08425 | + | 4.52950i | 0.302472 | + | 0.150816i | ||||
\(903\) | −37.7530 | −1.25634 | ||||||||
\(904\) | −11.4772 | + | 8.33870i | −0.381727 | + | 0.277341i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.22919 | + | 3.78307i | −0.0408372 | + | 0.125684i | ||||
\(907\) | −20.5284 | − | 14.9147i | −0.681634 | − | 0.495236i | 0.192266 | − | 0.981343i | \(-0.438417\pi\) |
−0.873899 | + | 0.486107i | \(0.838417\pi\) | |||||||
\(908\) | −1.03542 | − | 0.752278i | −0.0343617 | − | 0.0249652i | ||||
\(909\) | 1.32621 | − | 4.08166i | 0.0439877 | − | 0.135380i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.0825 | − | 10.2316i | 0.466575 | − | 0.338986i | −0.329530 | − | 0.944145i | \(-0.606890\pi\) |
0.796105 | + | 0.605159i | \(0.206890\pi\) | |||||||
\(912\) | 0.247229 | 0.00818657 | ||||||||
\(913\) | 0.733807 | + | 0.365884i | 0.0242855 | + | 0.0121090i | ||||
\(914\) | −6.12971 | −0.202753 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.47000 | + | 13.7573i | 0.147693 | + | 0.454553i | ||||
\(917\) | −16.1389 | + | 49.6704i | −0.532953 | + | 1.64026i | ||||
\(918\) | 0.0187264 | + | 0.0136055i | 0.000618062 | + | 0.000449048i | ||||
\(919\) | 26.6133 | + | 19.3357i | 0.877890 | + | 0.637825i | 0.932692 | − | 0.360673i | \(-0.117453\pi\) |
−0.0548022 | + | 0.998497i | \(0.517453\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.82072 | + | 27.1474i | 0.290653 | + | 0.894537i | ||||
\(922\) | −1.04666 | + | 0.760446i | −0.0344701 | + | 0.0250440i | ||||
\(923\) | −5.22245 | −0.171899 | ||||||||
\(924\) | 3.02381 | − | 20.2297i | 0.0994762 | − | 0.665507i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 5.72337 | − | 4.15827i | 0.188082 | − | 0.136649i | ||||
\(927\) | −0.646712 | − | 1.99038i | −0.0212408 | − | 0.0653725i | ||||
\(928\) | 3.46918 | − | 10.6770i | 0.113881 | − | 0.350491i | ||||
\(929\) | −26.9509 | − | 19.5810i | −0.884230 | − | 0.642431i | 0.0501368 | − | 0.998742i | \(-0.484034\pi\) |
−0.934367 | + | 0.356311i | \(0.884034\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.0680360 | + | 0.209393i | −0.00222979 | + | 0.00686258i | ||||
\(932\) | 6.28115 | + | 19.3314i | 0.205746 | + | 0.633221i | ||||
\(933\) | −8.04812 | + | 5.84730i | −0.263484 | + | 0.191432i | ||||
\(934\) | 6.21211 | 0.203266 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.15474 | −0.0377438 | ||||||||
\(937\) | −19.3061 | + | 14.0267i | −0.630704 | + | 0.458233i | −0.856644 | − | 0.515908i | \(-0.827455\pi\) |
0.225940 | + | 0.974141i | \(0.427455\pi\) | |||||||
\(938\) | −2.46979 | − | 7.60123i | −0.0806415 | − | 0.248189i | ||||
\(939\) | −5.07744 | + | 15.6267i | −0.165696 | + | 0.509959i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.41192 | + | 4.65853i | 0.209023 | + | 0.151864i | 0.687371 | − | 0.726306i | \(-0.258765\pi\) |
−0.478349 | + | 0.878170i | \(0.658765\pi\) | |||||||
\(942\) | −1.20642 | + | 3.71297i | −0.0393072 | + | 0.120975i | ||||
\(943\) | 23.9887 | + | 73.8297i | 0.781181 | + | 2.40423i | ||||
\(944\) | −5.33514 | + | 3.87620i | −0.173644 | + | 0.126160i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.21019 | + | 7.33681i | −0.234423 | + | 0.238540i | ||||
\(947\) | 2.15429 | 0.0700050 | 0.0350025 | − | 0.999387i | \(-0.488856\pi\) | ||||
0.0350025 | + | 0.999387i | \(0.488856\pi\) | |||||||
\(948\) | −1.23635 | + | 0.898262i | −0.0401548 | + | 0.0291742i | ||||
\(949\) | 2.47731 | + | 7.62439i | 0.0804170 | + | 0.247498i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.4966 | − | 8.35278i | −0.372803 | − | 0.270858i | ||||
\(952\) | 0.235096 | + | 0.170807i | 0.00761951 | + | 0.00553590i | ||||
\(953\) | 1.85195 | − | 5.69971i | 0.0599904 | − | 0.184632i | −0.916570 | − | 0.399874i | \(-0.869054\pi\) |
0.976561 | + | 0.215242i | \(0.0690540\pi\) | |||||||
\(954\) | −0.0707268 | − | 0.217675i | −0.00228986 | − | 0.00704748i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −32.9770 | −1.06655 | ||||||||
\(957\) | −12.2205 | + | 2.04472i | −0.395032 | + | 0.0660964i | ||||
\(958\) | −3.54816 | −0.114636 | ||||||||
\(959\) | 19.9767 | − | 14.5139i | 0.645082 | − | 0.468680i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.8096 | − | 57.8901i | 0.606762 | − | 1.86742i | ||||
\(962\) | −1.97959 | − | 1.43826i | −0.0638246 | − | 0.0463713i | ||||
\(963\) | −12.7347 | − | 9.25228i | −0.410369 | − | 0.298151i | ||||
\(964\) | 9.97085 | − | 30.6871i | 0.321139 | − | 0.988365i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.51067 | + | 3.27719i | −0.145128 | + | 0.105442i | ||||
\(967\) | −22.2784 | −0.716424 | −0.358212 | − | 0.933640i | \(-0.616613\pi\) | ||||
−0.358212 | + | 0.933640i | \(0.616613\pi\) | |||||||
\(968\) | −6.82729 | − | 9.06097i | −0.219437 | − | 0.291231i | ||||
\(969\) | 0.00607286 | 0.000195088 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.3381 | − | 34.8952i | −0.363858 | − | 1.11984i | −0.950693 | − | 0.310133i | \(-0.899626\pi\) |
0.586835 | − | 0.809706i | \(-0.300374\pi\) | |||||||
\(972\) | 0.596764 | − | 1.83665i | 0.0191412 | − | 0.0589106i | ||||
\(973\) | −52.1541 | − | 37.8922i | −1.67198 | − | 1.21477i | ||||
\(974\) | −1.83112 | − | 1.33039i | −0.0586728 | − | 0.0426283i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.1658 | − | 34.3649i | −0.357409 | − | 1.09999i | ||||
\(977\) | 22.5751 | − | 16.4018i | 0.722242 | − | 0.524739i | −0.164858 | − | 0.986317i | \(-0.552717\pi\) |
0.887100 | + | 0.461578i | \(0.152717\pi\) | |||||||
\(978\) | 0.892323 | 0.0285333 | ||||||||
\(979\) | −47.6894 | + | 7.97935i | −1.52416 | + | 0.255021i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.34343 | − | 2.42915i | 0.106748 | − | 0.0775567i | ||||
\(982\) | −2.10036 | − | 6.46424i | −0.0670252 | − | 0.206282i | ||||
\(983\) | −3.02596 | + | 9.31294i | −0.0965130 | + | 0.297037i | −0.987645 | − | 0.156708i | \(-0.949912\pi\) |
0.891132 | + | 0.453744i | \(0.149912\pi\) | |||||||
\(984\) | 9.73387 | + | 7.07207i | 0.310305 | + | 0.225449i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.0267218 | − | 0.0822412i | 0.000850995 | − | 0.00261909i | ||||
\(987\) | 0.896084 | + | 2.75786i | 0.0285227 | + | 0.0877837i | ||||
\(988\) | −0.120403 | + | 0.0874779i | −0.00383053 | + | 0.00278304i | ||||
\(989\) | −78.6678 | −2.50149 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.9794 | 1.11116 | 0.555578 | − | 0.831464i | \(-0.312497\pi\) | ||||
0.555578 | + | 0.831464i | \(0.312497\pi\) | |||||||
\(992\) | 23.3024 | − | 16.9302i | 0.739851 | − | 0.537533i | ||||
\(993\) | 3.37196 | + | 10.3778i | 0.107006 | + | 0.329331i | ||||
\(994\) | −1.20770 | + | 3.71692i | −0.0383059 | + | 0.117894i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.386258 | + | 0.280633i | 0.0122390 | + | 0.00889218i | ||||
\(997\) | 3.94779 | − | 12.1501i | 0.125028 | − | 0.384796i | −0.868878 | − | 0.495026i | \(-0.835159\pi\) |
0.993906 | + | 0.110230i | \(0.0351586\pi\) | |||||||
\(998\) | −2.27392 | − | 6.99839i | −0.0719795 | − | 0.221530i | ||||
\(999\) | 6.73928 | − | 4.89637i | 0.213221 | − | 0.154914i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 825.2.n.g.751.2 | 8 | ||
5.2 | odd | 4 | 825.2.bx.f.124.2 | 16 | |||
5.3 | odd | 4 | 825.2.bx.f.124.3 | 16 | |||
5.4 | even | 2 | 165.2.m.d.91.1 | ✓ | 8 | ||
11.2 | odd | 10 | 9075.2.a.cm.1.3 | 4 | |||
11.4 | even | 5 | inner | 825.2.n.g.301.2 | 8 | ||
11.9 | even | 5 | 9075.2.a.di.1.2 | 4 | |||
15.14 | odd | 2 | 495.2.n.a.91.2 | 8 | |||
55.4 | even | 10 | 165.2.m.d.136.1 | yes | 8 | ||
55.9 | even | 10 | 1815.2.a.p.1.3 | 4 | |||
55.24 | odd | 10 | 1815.2.a.w.1.2 | 4 | |||
55.37 | odd | 20 | 825.2.bx.f.499.3 | 16 | |||
55.48 | odd | 20 | 825.2.bx.f.499.2 | 16 | |||
165.59 | odd | 10 | 495.2.n.a.136.2 | 8 | |||
165.119 | odd | 10 | 5445.2.a.bt.1.2 | 4 | |||
165.134 | even | 10 | 5445.2.a.bf.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.d.91.1 | ✓ | 8 | 5.4 | even | 2 | ||
165.2.m.d.136.1 | yes | 8 | 55.4 | even | 10 | ||
495.2.n.a.91.2 | 8 | 15.14 | odd | 2 | |||
495.2.n.a.136.2 | 8 | 165.59 | odd | 10 | |||
825.2.n.g.301.2 | 8 | 11.4 | even | 5 | inner | ||
825.2.n.g.751.2 | 8 | 1.1 | even | 1 | trivial | ||
825.2.bx.f.124.2 | 16 | 5.2 | odd | 4 | |||
825.2.bx.f.124.3 | 16 | 5.3 | odd | 4 | |||
825.2.bx.f.499.2 | 16 | 55.48 | odd | 20 | |||
825.2.bx.f.499.3 | 16 | 55.37 | odd | 20 | |||
1815.2.a.p.1.3 | 4 | 55.9 | even | 10 | |||
1815.2.a.w.1.2 | 4 | 55.24 | odd | 10 | |||
5445.2.a.bf.1.3 | 4 | 165.134 | even | 10 | |||
5445.2.a.bt.1.2 | 4 | 165.119 | odd | 10 | |||
9075.2.a.cm.1.3 | 4 | 11.2 | odd | 10 | |||
9075.2.a.di.1.2 | 4 | 11.9 | even | 5 |